{"title":"Dynamic analysis and chaos control of a unified chaotic system","authors":"Xia Wu, Xiaoling Qiu, Limi Hu","doi":"10.1007/s12043-024-02744-z","DOIUrl":null,"url":null,"abstract":"<p>Two different control methods are proposed in this paper to effectively control the chaotic phenomenon of nonlinear dynamical system. One is a new Hamilton energy feedback control method based on Helmholtz’s theorem, which reduces the Lyapunov exponents value of the system by adjusting the feedback gain for controlling chaos. The other is to control the chaos of the system by using delayed feedback control method. Based on this method, we consider the local asymptotic stability of the equilibrium point of the system, and give conditions for the existence of the Hopf bifurcation of the system and the stability domain of the delay parameters. By using the centre manifold theorem and the Poincare normal form method, specific formulas for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions are derived. Finally, the simulation results show that chaos can be controlled by choosing appropriate time-delay parameters.\n</p>","PeriodicalId":743,"journal":{"name":"Pramana","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s12043-024-02744-z","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Two different control methods are proposed in this paper to effectively control the chaotic phenomenon of nonlinear dynamical system. One is a new Hamilton energy feedback control method based on Helmholtz’s theorem, which reduces the Lyapunov exponents value of the system by adjusting the feedback gain for controlling chaos. The other is to control the chaos of the system by using delayed feedback control method. Based on this method, we consider the local asymptotic stability of the equilibrium point of the system, and give conditions for the existence of the Hopf bifurcation of the system and the stability domain of the delay parameters. By using the centre manifold theorem and the Poincare normal form method, specific formulas for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions are derived. Finally, the simulation results show that chaos can be controlled by choosing appropriate time-delay parameters.
期刊介绍：
Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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